Algebra 7

4 marks · Normal

A number is chosen. The sum of the square of the number and 6 times the number is 40.

(a)

Let the number be . Write a quadratic equation for this problem.

[1 mark]

(b)

Solve the equation to find the value(s) of .

[2 marks]

(c)

State the value(s) of that solve the original problem.

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) x^2 + 6x = 40 or x^2 + 6x - 40 = 0

(b) x = 4 or x = -10

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Correct quadratic equation written for the problem.

M2 (b) · 1 mark · Attempts solving by factorising, quadratic formula or completing the square.

A1 (b) · 1 mark · States both solutions: and .

B1 (c) · 1 mark · Gives both values as valid solutions to the context.

Worked solution

Let the number be : , or .

Factorise: , so or .

Both values solve the original problem.